#include <iostream>
#include <cstring>
#include <algorithm>
#include <iomanip>
#include <set>
#include <vector>
#include <cstdio>
#include <cmath>
#define LL long long
#define nextLine() {int c = 0; while ((c = getchar()) != EOF && c != 10);}
#define sqr(a) ((a) * (a))
#define fill(a, c) memset(a, c, sizeof a)
#define ldb long double
#define sgn(a) ((a) > eps ? 1 : -1)
const ldb eps = 1e-9;
const ldb pi = fabs(atan2(0.0, -1.0));
const int INF = 1 << 28;
const LL LINF = 1ll << 50;
const ldb LDINF = 1e70;
const ldb cos3 = cos(pi / 3);
const ldb sin3 = sin(pi / 3);
using namespace std;
#define file ""



void Load()
{

}

void Solve()
{

}

int main()
{
	#ifndef ONLINE_JUDGE
	freopen(file".in", "rt", stdin);
	freopen(file".out", "wt", stdout);
	#endif
	Load();
	Solve();
	return 0;
}